Non-Equilibrium Sound Propagation in Discrete Velocity Models

Discrete velocity models developed by Gatignol are used to study the propagation properties of one-dimensional, plane sound waves in monatomic gases, which is fundamental in Rarefied Gases Dynamics and Nonequilibrium Thermodynamics. The governing equations for 4-, 6- and 8-velocity models are first linearized around a uniform state. Then, plane-wave solutions are found where the sound dispersion and attenuation are determined. The results show that only the 4-velocity model properly predicts the propagation of sound waves in the high Knudsen number regime in comparison with experimental data.